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# Ranking conflicts Answer: a Diff: E

## 56. NPV and IRR Answer: d Diff: E N

Use your financial calculator to solve for each project’s IRR:

Project X: CF_{0} = -500000; CF_{1} = 250000; CF_{2}
= 250000; CF_{3} = 250000; and then solve for IRR = 23.38%.

Project Y: CF_{0} = -500000; CF_{1} = 350000; CF_{2}
= 350000; and then solve for IRR = 25.69%.

Since Project Y has the higher IRR, use its data to solve for its NPV as follows:

CF_{0} = -500000; CF_{1} = 350000; CF_{2} =
350000; I/YR = 10; and then solve for NPV = $107,438.02.

57. NPV, IRR, and payback Answer: d Diff: E

Payback = 2 + $300/$500 = 2.6 years.

Using the cash flow register, calculate the NPV and IRR as follows:

Inputs: CF_{0} = -1000; CF_{1} = 400; CF_{2}
= 300; CF_{3} = 500; CF_{4} = 400; I = 10.

Outputs: NPV = $260.43 $260; IRR = 21.22%.

**58**

. Crossover rate Answer: b Diff: E

Financial calculator solution:

Solve for IRR_{A}:

Inputs: CF_{0} = -50000; CF_{1} = 15990; N_{j}
= 5. Output: IRR = 18.0%.

Solve for IRR_{B}:

Inputs: CF_{0} = -50000; CF_{1} = 0; N_{j}
= 4; CF_{2} = 100560.

Output: IRR = 15.0%.

Solve for crossover rate using the differential project CFs, CF_{A-B}

Inputs: CF_{0} = 0; CF_{1} = 15990; N_{j} =
4; CF_{2} = -84570.

Output: IRR = 11.49%. The crossover rate is 11.49%.

59**.** **Crossover
rate Answer: d Diff: E**

Find the crossover rate, which is the IRR of the difference in each
year’s cash flow from the two projects. The differences of the
cash flows (CF_{B} - CF_{A}) are entered into the
calculator:

CF_{0} = -100000; CF_{1} = 25000; CF_{2} =
25000; CF_{3} = 30000; CF_{4} = 50000; and then
solve for IRR = 10.03%.

**60**

**.** **Crossover rate Answer: a Diff: E**

Step 1: Determine the differential cash flows (in millions of dollars) between Projects X and Y:

Project X Project Y CFs

__Year__ __Cash Flow__ __Cash Flow__
__X - Y__

0 -$3,700 -$3,200 $-500

1 1,400 900 500

2 1,070 1,000 70

3 1,125 1,135 -10

4 700 720 -20

Step 2: Calculate the IRR of the differential cash flows:

Enter the following data in the calculator:

CF_{0} = -500; CF_{1} = 500; CF_{2} = 70;
CF_{3} = -10; CF_{4} = -20; and then solve for IRR =
8.073%.

61**.** **Crossover
rate Answer: c Diff: E**

Step 1: Determine the differential cash flows between Projects A and B:

Project A Project B CFs

__Year__ __Cash Flow__ __Cash Flow__
__A - B__

0 -$2,000 -$1,500 -$500

1 700 300 400

2 700 500 200

3 1,000 800 200

4 1,000 1,100 -100

Step 2: Calculate the IRR of the differential cash flows:

Enter the following data in the calculator:

CF_{0}
= -500; CF_{1}
= 400; CF_{2}
= 200; CF_{3}
= 200; CF_{4}
= -100; and then solve for IRR = 26.67%.

## 62. Crossover rate Answer: d Diff: E N

First, we must find the difference in the 2 projects’ cash flows for each year.

Project 1 Project 2 CFs

__Year__ __Cash Flow__ __Cash Flow__ __1 - 2__

0 -$400 -$500 $100

1 175 50 125

2 100 100 0

3 250 300 -50

4 175 550 -375

Then, enter these data into the cash flow register on your calculator and solve for IRR:

CF_{0} = 100; CF_{1} = 125; CF_{2} = 0; CF_{3}
= -50; CF_{4} = -375; and then solve for IRR = 20.97%.

### 63. Crossover rate Answer: d Diff: E N

This is simply asking for the crossover rate of these two projects. The first step to finding the crossover rate is to take the difference of the two projects’ cash flows. Here, we subtracted the second column from the first:

Project A Project B CFs

__Year__ __Cash Flow__ __Cash Flow__ __A - B__

0 -$300 -$300 $0

1 140 500 -360

2 360 150 210

3 400 100 300

To find the crossover rate, enter the
cash flows in the cash flow register: CF_{0} = 0; CF_{1}
= -360; CF_{2} = 210; CF_{3} = 300; and then solve
for IRR = 25.00%.

64. Payback period Answer: c Diff: M

Payback = 5 + = 5.928 years 6 years.

## 65. Payback period Answer: c Diff: M

Step 1: Calculate the PV of the cash flows:

Inputs: N = 5; I = 10; PMT = 60000; FV =0.

Output: PV = -$227,447.21. PV of cash flows = $227,447.21 ≈ $227,447.

Step 2: Calculate the Year 0 outflow:

The outflow at t = 0 is X where $227,447 - X = $75,000. X or CF_{0}
= -$152,447.

Step 3: Calculate the regular payback:

__Year__ __ CF __ __Cumulative CF__

0 -$152,447 -$152,447

1 60,000 -92,447

2 60,000 -32,447

3 60,000 27,553

4 60,000 87,553

5 60,000 147,553

So the payback is 2 + = 2.54 years.

66. Discounted payback Answer: e Diff: M

Discounted

__Year__ __ Cash Flow __ __Cash Flow @ 10%__ __Cumulative
PV__

0 -$200,000 -$200,000.00 -$200,000.00

1 50,000 45,454.55 -154,545.45

2 100,000 82,644.63 -71,900.82

3 150,000 112,697.22 40,796.40

4 40,000 27,320.54 68,116.94

5 25,000 15,523.03 83,639.97

Payback period = 2 years + = 2.638 years.

**67**

. Discounted payback Answer: b Diff: M

Discounted

__Year__ __ Cash Flow __ __Cash Flow @ 10%__ __Cumulative
PV__

0 -$100,000 -$100,000.00 -$100,000.00

1 40,000 36,363.64 -63,636.36

2 90,000 74,380.17 10,743.81

3 30,000 22,539.44 33,283.25

4 60,000 40,980.81 74,264.06

Discounted Payback = 1 + = 1.86 years.

**68**

. Discounted payback Answer: d Diff: M

Project A:

Discounted

__Year__ __ Cash Flow __ __Cash Flow @ 10%__ __Cumulative
PV__

0 -$100,000 -$100,000.00 -$100,000.00

1 40,000 36,363.64 -63,636.36

2 40,000 33,057.85 -30,578.51

3 40,000 30,052.59 -525.92

4 30,000 20,490.49 19,964.57

Project A’s discounted payback period exceeds 3 years, so it would not be accepted.

Project B:

Discounted

__Year__ __ Cash Flow __ __Cash Flow @ 10%__ __Cumulative
PV__

0 -$80,000 -$80,000.00 -$80,000.00

1 50,000 45,454.55 -34,545.45

2 20,000 16,528.93 -18,016.52

3 30,000 22,539.44 4,522.92

4 0 0 4,522.92

You can see that in Year 3 the cumulative cash flow becomes positive so the project’s payback period is less than 3 years.

69. NPV Answer: d Diff: M

Financial calculator solution (in thousands):

Inputs: CF_{0} = -150; CF_{1} = 30; N_{j} =
4; CF_{2} = 35; N_{j} = 5; CF_{3} = 40; I =
10.

Output: NPV = $51.13824 = $51,138.24 $51,138.

**70**

. NPV Answer: b Diff: M

Financial calculator solution (in thousands):

Inputs: CF_{0} = 0; CF_{1} = 5; N_{j} = 5;
CF_{2} = 3; N_{j} = 3; CF_{3} = 2; N_{j}
= 2; I_{ }=_{ }14.

Output: NPV = 21.93726 = $21,937.26.

## 71. NPV Answer: d Diff: M N

First, find the value of X (the up-front cash flow in this project). IRR is the rate at which you need to reinvest the cash flows for NPV to equal $0. In this case the IRR is 12 percent, so if you invest all the project’s cash flows at 12 percent, you should have an NPV of zero.

Step 1: Calculate the value of the initial cash flow by solving for NPV at a 12 percent cost of capital:

You don’t have CF_{0}, so use 0 as the placeholder. Enter
the following data as inputs in your calculator: CF_{0} =
0; CF_{1} = 75000; N_{j} = 20; and I/Yr = 12. Then
solve for NPV = $560,208.27.

This is the NPV when the initial cash flow is missing. The NPV when
the cash flow is added must be $0, so that initial cash flow must be

–$560,208.27.

Step 2: Calculate the net present value of the project at its cost of capital of 10 percent:

Enter the following data as inputs in your calculator: CF_{0}
=

-560208.27; CF_{1} = 75000; N_{j} = 20; and
I/Yr = 10. Then solve for NPV = $78,309.01
$78,309.

72. NPV profiles Answer: d Diff: M

First, solve for the crossover rate. If you subtract the cash flows
(CFs) of Project A from the CFs of Project B, then the differential
CFs are CF_{0} = -10000, CF_{1} = -40000, CF_{2}
= 0, CF_{3} = 20000, and CF_{4} = 40000. Entering
these CFs and solving for IRR/YR yields a crossover rate of 6.57%.
Thus, if the cost of capital is 6.57%, then Projects A and B have
the same NPV. If the cost of capital is less than 6.57%, then
Project B has a higher NPV than Project A, since Project B’s cash
inflows come comparatively later in the project life. For lower
discount rates, Project B’s NPV is not penalized as much for
having large cash inflows farther in the future than Project A.

73. NPV, payback, and missing cash flow Answer: b Diff: M

First, find the missing t = 0 cash flow. If payback = 2.5 years,
this implies t_{ }=_{ }0 cash flow must be -$2,000_{
}- $3,000 + (0.5)$3,000 = -$6,500.

NPV = -$6,500 + + + +

= $765.91.

74. IRR Answer: d Diff: M

Financial calculator solution:

Machine A: Inputs: CF_{0} = -2000; CF_{1} = 0; N_{j}
= 3; CF_{2} = 3877.

Output: IRR = 17.996% 18%.

Machine B: Inputs: CF_{0} = -2000; CF_{1} = 832; N_{j}
= 4.

Output: IRR = 24.01% 24%.

**75**

. IRR Answer: c Diff: M

Financial calculator solution:

Project A: Inputs: N = 1; PV = -10000; PMT = 0; FV = 11800.

Output: I = 18% = IRR_{A}.

Project C: Inputs: N = 3; PV = -12000; PMT = 5696; FV = 0.

Output: I = 19.99% 20% =
IRR_{C}.

## 76. IRR Answer: e Diff: M N

Using your financial calculator find the NPV without the initial cash flow:

CF_{0} = 0; CF_{1} = 150; CF_{2} = 200; CF_{3}
= 250; CF_{4} = 400; CF_{5} = 100; I = 10; and then
solve for NPV = $824.78.

This means that the initial cash flow must be –700 ($124.78 -
$824.78 =

-$700). Now,
we can
enter all
the cash flows and solve for the project’s IRR.

CF_{0} = -700; CF_{1} = 150; CF_{2} = 200;
CF_{3} = 250; CF_{4} = 400; CF_{5} = 100;
and then solve for IRR = 16.38%.

77. NPV and IRR Answer: a Diff: M

Project S: Inputs: CF_{0} = -1100; CF_{1} = 900;
CF_{2} = 350; CF_{3} = 50; CF_{4} = 10;

I = 12.

Outputs: NPV_{S} = $24.53; IRR_{S} =
13.88%.

Project L: Inputs: CF_{0} = -1100; CF_{1} = 0;
CF_{2} = 300; CF_{3} = 500; CF_{4} = 850;

I = 12.

Outputs: NPV_{L} = $35.24; IRR_{L} =
13.09%.

Project L has the higher NPV and its IRR = 13.09%.

**78**

. IRR of uneven CF stream Answer: d Diff: M

Financial calculator solution (in millions):

Inputs: CF_{0} = -3; CF_{1} = 2; N_{j} = 2;
CF_{2} = -0.5.

Output: IRR = 12.699% 12.70%.

**79**

. IRR of uneven CF stream Answer: e Diff: M

Financial calculator solution (in millions):

Inputs: CF_{0} = -5; CF_{1} = 1.0; CF_{2} =
1.5; CF_{3} = 2.0; N_{j} = 3.

Output: IRR = 18.37%.

80**.** **IRR,
payback, and missing cash flow Answer: c Diff: M**

Step 1: Find Project 1’s payback:

Project 1 Cumulative

__Year__ __Cash Flow__ __Cash Flow __

0 -100 -100

1 30 -70

2 50 -20

3 40 20

4 50 70

Payback_{Project 1} = 2 + $20/$40 = 2.5 years.

Project 2’s payback = 2.5 years because we’re told the two projects’ paybacks are equal.

Step 2: Calculate Project 2’s initial outlay, given its payback = 2.5 years:

Initial outlay = -[CF_{1} + CF_{2} + (0.5)(CF_{3})]

= -[$40 + $80 + (0.5)($60)]

= -$150.

Step 3: Calculate Project 2’s IRR:

Enter the following data in the calculator:

CF_{0} = -150; CF_{1} = 40; CF_{2} = 80; CF_{3}
= 60; CF_{4} = 60; and then solve for IRR = 20.85%.

81. MIRR Answer: d Diff: M

Financial calculator solution:

TV Inputs: N = 8; I = 12; PV = 0; PMT = 73306.

Output: FV = -$901,641.31.

MIRR Inputs: N = 8; PV = -275000; PMT = 0; FV = 901641.31.

Output: I = 16.0%.

82. MIRR Answer: e Diff: M

Step 1: Find the FV of cash inflows:

($25,000)(1.12)^{4} = $ 39,337.98

( 25,000)(1.12)^{3} = 35,123.20

( 50,000)(1.12)^{2} = 62,720.00

( 50,000)(1.12) = 56,000.00

( 50,000)(1.12)^{0} = __ 50,000.00__

Future Value = __$243,181.18__

Alternatively, with a financial calculator you can find the FV of the cash inflows by first finding the NPV of these inflows and then finding the FV of their NPV.

CF_{0} = 0; CF_{1-2} = 25000; CF_{3-5} =
50000; I = 12; and then solve for NPV = $137,987.53.

N = 5; I = 12; PV = -137987.53; PMT = 0; and then solve for FV = $243,181.18.

Step 2: Find the MIRR, which is the discount rate that equates the cash inflows and outflows:

N = 5; PV = -100000; PMT = 0; FV = 243181.18; and then solve for I = MIRR = 19.45%.

83. MIRR and CAPM Answer: d Diff: M R

Step 1: Calculate the historical beta:

Regression method: Financial calculator: Different calculators have different list entry procedures and key stroke sequences.

Enter Y-list: Inputs: Item(1) = 9 INPUT; Item(2) = 15 INPUT; Item(3) = 36 INPUT.

Enter X-list: Inputs: Item(1) = 6 INPUT; Item(2) = 10 INPUT; Item(3) = 24 INPUT; use linear model.

Output: m or slope = 1.50.

Graphical/numerical method:

Slope = Rise/Run = (36% - 9%)/(24% - 6%) = 27%/18% = 1.5. Beta = 1.5.

Step 2: Calculate cost of equity using CAPM and beta and given inputs:

k_{e} = k_{RF} + (RP_{M})Beta = 7.0% +
(6%)1.5 = 16.0%.

Step 3: Calculate TV of inflows:

Inputs: N = 3; I = 16; PV = 0; PMT = 1000.

Output: FV = -$3,505.60.

Step 4: Calculate MIRR:

Inputs: N = 3; PV = -2028; PMT = 0; FV = 3505.60.

Output: I = 20.01 = MIRR 20%.